The design of high-resolution upwind shock-capturing methods

Thesis/Dissertation · Mon Jun 01 04:00:00 EDT 1992

OSTI ID:10156739

Rider, W J

The design and construction of high-resolution upwind shock-capturing methods is an effective means of solving conservation laws of physics numerically. In the past, the design of such methods was generally categorized into several distinct methods. This work shows how these methods can be viewed in a unified manner. A generalized flux-corrected transport (FCT) algorithm is shown to be total variation diminishing (TVD) under some conditions. The new algorithm has improved properties from the standpoint of use and analysis. This is shown to be especially important for systems of equations. The new formulation allows Riemann solvers to be used effectively with FCT methods. This directly leads to a geometric analog to symmetric TVD and FCT methods that is developed and expanded upon. This unifies these methods with high-order Godunov (HOG) methods. Two new variants of this are derived and shown to be uniformly non-oscillatory. Limiters are an effective means of designing these types of methods. More general classes of limiters are discussed with extensions to a wider class of schemes. Flux-corrected transport and total variation bounded (TVB) limiters are discussed, modified, and expanded. Two new classes of limiters are described: s-limiters and generalized average limiters. The recently defined ULTIMATE limiter is analyzed within the framework of the other limiters. The benefits of relaxing strict constraints on the limiters such as TVD requirements are also discussed. For coarse grids, limiters such as the TVB and the generalized average with bias improve resolution considerably. Lastly, the question of whether the polynomial reconstruction technique used in a HOG method should be based on cell-averages or point-values is studied.

• Research Organization: Los Alamos National Lab., NM (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: AC04-76DP00789
• OSTI ID: 10156739
• Report Number(s): LA--12327-T; ON: DE92016866
• Country of Publication: United States
• Language: English

Related Subjects

661300
662120
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
99 GENERAL AND MISCELLANEOUS
990200
ALGORITHMS
CONSERVATION LAWS
DIFFERENTIAL CALCULUS
INTEGRAL CALCULUS
MATHEMATICS AND COMPUTERS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
OTHER ASPECTS OF PHYSICAL SCIENCE
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICS
RUNGE-KUTTA METHOD
SYMMETRY
CONSERVATION LAWS
CURRENTS AND THEIR PROPERTIES